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Features of POLLUSOL Flow model Flow model Homogeneous, Isotropic, Heterogeneous and Anisotropic medium Homogeneous, Isotropic, Heterogeneous and Anisotropic medium Saturated as well as Unsaturated subsurface environment Saturated as well as Unsaturated subsurface environment Multiple layers Multiple layers Transient and Steady flow simulation Transient and Steady flow simulation Pressure head and / or Flux boundary conditions Pressure head and / or Flux boundary conditions

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Features of POLLUSOL (contd..) Solute transport model Solute transport model Multiple layers Multiple layers Forecasting of the future effects of groundwater pollution Forecasting of the future effects of groundwater pollution Homogeneous, Isotropic, Heterogeneous and Anisotropic medium Homogeneous, Isotropic, Heterogeneous and Anisotropic medium Saturated as well as Unsaturated subsurface environments Saturated as well as Unsaturated subsurface environments Constant concentration and/or Flux boundary conditions Constant concentration and/or Flux boundary conditions Transient and Steady state simulation Transient and Steady state simulation

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CASE STUDIES (Flow cases) 4. Earth and rock-fill dam using Gardner permeability function (nonhomogeneous earth and rock-fill dam) 1. Flow around the cylinder 3. Steady-state seepage analysis through saturated- unsaturated soils 2. Confined flow under dam foundation

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Case1: Flow around the cylinder Introduction Introduction This study examines the problem of uniform fluid flow around a cylinder of unit radius, θ r X Y Φ1Φ1 Φ2Φ2 L L

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Analytically, The total head values at any point in the problem domain can be given as : U is the uniform undisturbed velocity = a is the radius of cylinder, is the anti-clockwise angle measured from the x-axis to the field point is the anti-clockwise angle measured from the x-axis to the field point

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Owing to the symmetry of problem only half of domain is discretized in the model

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Mesh Mesh 2-dimensional zone with quadrilateral elements which comprises of 223 cells and 472 nodes 2-dimensional zone with quadrilateral elements which comprises of 223 cells and 472 nodes Porous Medium Porous Medium Fully saturated material with hydraulic conductivity of 1e-05 m/s Fully saturated material with hydraulic conductivity of 1e-05 m/s Water Water Incompressible with density=1000 Kg/m 3 Incompressible with density=1000 Kg/m 3

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Boundary conditions Boundary conditions Constant head of 1 m is applied at the left boundary and Zero head is applied at right boundary The remaining boundaries are no flow boundaries those could be considered as adiabatic walls.

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Results Results Flow vector (m/s) with mesh Flow vector (m/s) with mesh

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Total pressure head (m) contours in the domain

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Comparison of total heads calculated using Pollusol with that of other Models Coordinates of points on problem domain PollusolPhase2*analyticalRef.** XY 410.5850.49990.50000.500 4.50.8660.3880.38100.37430.3780 500.2550.26260.25000.2765 600.190.20310.18750.2132 800.0560.0000-0.03120.000 * Groundwater Module in Phase2, 2D finite element program for ground water analysis, Version 6.0, 2005, Rocscience Inc. ** Desai, C. S., Kundu T., (2001) Introductory Finite Element Method, Boca Ration, Fla. CRC Press

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Case2: Confined flow under dam foundation Introduction Introduction It examines the confined flow under dam which rest on homogeneous isotropic soil with dimensions (40m*10m).The walls and base of dam are considered impervious

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Mesh Mesh The domain is modeled as a 2-dimensional zone with quadrilateral elements. The mesh comprises of 10800 cells and 15004 nodes Porous Medium Porous Medium Fully saturated material with hydraulic conductivity of 1e-05 m/s Water Water Incompressible with density=1000 Kg/m 3

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Boundary conditions Boundary conditions No flow occurs across the impermeable surfaces. These were considered as isotropic walls. No flow occurs across the impermeable surfaces. These were considered as isotropic walls. Total pressure head between A and B is equal to 5 m and between C and D is equal to 0.0 m. Total pressure head between A and B is equal to 5 m and between C and D is equal to 0.0 m.

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Results Results Flow vector (m/s) with mesh Flow vector (m/s) with mesh

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Total pressure head (m) contours in the domain Total pressure head (m) contours in the domain

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Comparison of total head variation along section 1-1 obtained using Pollusol with that of other models Pollusol Phase2* and Ref** Groundwater Module in Phase2, 2D finite element program for ground * Groundwater Module in Phase2, 2D finite element program for ground water analysis, Version 6.0, 2005, Rocscience Inc. ** Rushton K.R., Redshaw S.C. (1979) Seepage and Groundwater Flow, John Wiley & Sons, U.K.

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Comparison of total head variation along section 2-2 obtained using Pollusol with that of other models Pollusol Phase2* and Ref** * Groundwater Module in Phase2, 2D finite element program for ground water analysis, Version 6.0, 2005, Rocscience Inc. ** Rushton K.R., Redshaw S.C. (1979) Seepage and Groundwater Flow, John Wiley & Sons, U.K.

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Case3: Steady-state seepage analysis through saturated-unsaturated soils Introduction Introduction This study considers the problem of seepage through an earth dam.

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Mesh Mesh The domain is modeled as a 2-dimensional zone with quadrilateral elements. The mesh comprises of 1404 cells and 2906 nodes Water Water Incompressible with density=1000 Kg/m 3

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Porous Medium Porous Medium Four types of cases are considered: Four types of cases are considered: 1. Isotropic earth dam with a horizontal drain (length 12 m) 2. Anisotropic earth dam with a horizontal drain 3. Isotropic earth dam with a core and horizontal drain 4. Isotropic earth dam with a steady state infiltration 5. Isotropic earth dam with a seepage face

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For Anisotropic earth dam horizontal direction is nine times larger than in the vertical direction. The permeability function for vertical direction is same as that of isotropic earth dam. The permeability function used for isotropic earth dam

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An isotropic dam having core with lower coefficient of permeability. The permeability function used for the core of the dam

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Boundary conditions Boundary conditions 1. Isotropic earth dam with a horizontal drain Total head of 10m at the left side. Total head of 10m at the left side. Zero pressure head at horizontal drain. Zero pressure head at horizontal drain. No flow occurs at the rest of the boundary of geometry that could be considered as adiabatic walls in model. No flow occurs at the rest of the boundary of geometry that could be considered as adiabatic walls in model. 2. Anisotropic earth dam with a horizontal drain Same as that of case1. Same as that of case1. 3. Isotropic earth dam with a core and horizontal drain Same as that of case1. Same as that of case1.

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Boundary conditions (contd..) Boundary conditions (contd..) 3. Isotropic earth dam with a steady state infiltration Total head of 10m applied at the left side Total head of 10m applied at the left side Flux boundary of 1e-8 m/s applied at the right side in order to consider the effect of infiltration Flux boundary of 1e-8 m/s applied at the right side in order to consider the effect of infiltration Zero pressure head at horizontal drain Zero pressure head at horizontal drain No flow occurs at the rest of the boundary of the geometry that could be considered as adiabatic walls in model No flow occurs at the rest of the boundary of the geometry that could be considered as adiabatic walls in model 4. Isotropic earth dam with a seepage face Total head of 10m applied at the left side of the dam Total head of 10m applied at the left side of the dam Pressure is zero at right bottom of the slope surface Pressure is zero at right bottom of the slope surface No flow occurs at the rest of the boundary of the geometry that could be considered as adiabatic walls in model No flow occurs at the rest of the boundary of the geometry that could be considered as adiabatic walls in model

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Results Isotropic earth dam with a horizontal drain Isotropic earth dam with a horizontal drain Flow vector (m/s) with mesh

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Total pressure head (m) contours in the domain Total pressure head (m) contours in the domain

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Total pressure head along the section1-1 Total pressure head along the section1-1

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Anisotropic earth dam with a horizontal drain Anisotropic earth dam with a horizontal drain Flow vector (m/s) with mesh

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Total pressure head (m) contours in the domain Total pressure head (m) contours in the domain

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Total pressure head along the section1-1 Total pressure head along the section1-1

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Isotropic earth dam with a core and horizontal drain Isotropic earth dam with a core and horizontal drain Flow vector (m/s) with mesh

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Total pressure head (m) profile in the domain Total pressure head (m) profile in the domain

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Total pressure head along the section1-1 Total pressure head along the section1-1

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Isotropic earth dam with a steady state infiltration Isotropic earth dam with a steady state infiltration Flow vector (m/s) with mesh

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Total pressure head (m) contours in the domain Total pressure head (m) contours in the domain

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Total pressure head along the section1-1 Total pressure head along the section1-1

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Isotropic earth dam with a seepage face Isotropic earth dam with a seepage face Flow vector (m/s) with mesh

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Total pressure head (m) contours in the domain Total pressure head (m) contours in the domain

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Total pressure head along the section1-1 Total pressure head along the section1-1

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Case4: Earth and rock-fill dam using Gardner permeability function (nonhomogeneous earth and rock-fill dam) Introduction Introduction This study examines seepage flow rate through the nonhomgeneous earth and rock fill dam.

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Mesh Mesh The domain is modeled as a 2-dimensional zone with triangular elements. The mesh comprises of 3616 cells and 3890 nodes Water Water Incompressible with density=1000 Kg/m 3

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Porous Medium Porous Medium The porous medium was unsaturated. Gardner non- linear equation between permeability function and pressure head was used as given below where a and n are the model parameters, h is pressure head (suction), h is pressure head (suction), K u is unsaturated permeability, and K u is unsaturated permeability, and K s is saturated permeability. K s is saturated permeability.

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LayerK s (m/s)an Dam1e-70.152 Foundation1.25e-50.156 Toe drain1e-30.156 Models parameters used

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Boundary conditions Boundary conditions Total pressure head of 28 m was applied at the left of the dam Total pressure head of 28 m was applied at the left of the dam Total pressure head of 10 m was considered at the right of the dam. Total pressure head of 10 m was considered at the right of the dam. No flow was occurred at the rest boundaries of the geometry that could be treated as adiabatic walls No flow was occurred at the rest boundaries of the geometry that could be treated as adiabatic walls

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Results Results Flow vector with mesh Flow vector with mesh

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Total pressure head contours in the domain Total pressure head contours in the domain

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1. Areal Constant Density Solute Transport (Example at Rocky Mountain Arsenal) 2. Three-dimensional contaminant transport through the porous medium CASE STUDIES (Flow and Solute transport cases)

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Case1: Areal Constant Density Solute Transport (Example at Rocky Mountain Arsenal) Introduction Introduction It consists of an areal model of a rectangular alluvial aquifer with a constant transmissivity and two impermeable bedrock outcrops which influence groundwater flow. It consists of an areal model of a rectangular alluvial aquifer with a constant transmissivity and two impermeable bedrock outcrops which influence groundwater flow. Three wells pump from the aquifer (at a rate of Q OUT each), and contamination enters the system through a leaking waste isolation pond (at a rate of Q IN, with concentration, C). Three wells pump from the aquifer (at a rate of Q OUT each), and contamination enters the system through a leaking waste isolation pond (at a rate of Q IN, with concentration, C).

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Mesh Mesh The domain is modeled as a 2-dimensional zone with quadrilateral elements. The mesh comprises of 32000 cells and 64722 nodes Water Water Incompressible with density=1000 Kg/m 3 Viscosity of water =0.001 Pa.s

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Parameters used Parameters used Porosity (n)=0.2 Porosity (n)=0.2 Hydraulic conductivity (K x = K y = K z ) = 7.76e-12 m 2Hydraulic conductivity (K x = K y = K z ) = 7.76e-12 m 2 Longitudinal dispersivity (α L ) = 152.4 mLongitudinal dispersivity (α L ) = 152.4 m Transverse dispersivity (α T ) = 30.48 mTransverse dispersivity (α T ) = 30.48 m Leakage rate through pond (Q IN ) = 0.0283 m 3 /sLeakage rate through pond (Q IN ) = 0.0283 m 3 /s Concentration entered through pond (C) = 1000 ppmConcentration entered through pond (C) = 1000 ppm Pumping rate from each well (Q OUT ) = 0.005663 m 3 /sPumping rate from each well (Q OUT ) = 0.005663 m 3 /s Half life period = 20 yearsHalf life period = 20 years

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Initial conditions Initial conditions Initial pressures are zero for steady-state simulation of pressure. Initial concentration is zero ppm Initial pressures are zero for steady-state simulation of pressure. Initial concentration is zero ppm Boundary conditions Boundary conditions No flow occurs across any boundary except where constant heads are specified at 76.2 m and 11.43 m at the top of the mesh and at the bottom of the mesh respectively. No flow occurs across any boundary except where constant heads are specified at 76.2 m and 11.43 m at the top of the mesh and at the bottom of the mesh respectively. A source is specified at the leaky pond node, and a sink is specified at each well node. A source is specified at the leaky pond node, and a sink is specified at each well node.

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Results Total Pressure head contours

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Solute concentration contours after 1000 years

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Solute concentration (with solute half life ~ 20 years) after 1000 years

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Case2: Three-dimensional contaminant transport through the porous medium Introduction Introduction The study area consists of homogeneous and isotropic confined aquifer. A horizontal source 200m*100m*0.1m (i.e. red color indicated in figure 1.0) on the upper surface of the computational domain continuously releases a contaminant into the aquifer, which is initially free of the contaminant 3700m 800m 56m 700m 200m 100m

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Mesh Mesh The domain is modeled as a 2-dimensional zone with hexa elements. The mesh comprises of 80000 cells and 23042 nodes Water Water Incompressible with density = 1000 Kg/m 3 Viscosity of water = 0.001 Pa.s

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Parameters Parameters Porosity of the porous medium=0.1 Porosity of the porous medium=0.1 Longitudinal dispersivity = 91 m Longitudinal dispersivity = 91 m Transverse dispersivity = 20 m Transverse dispersivity = 20 m The release of contaminant in to aquifer is 2.5e -4 kg/m 3 s. The release of contaminant in to aquifer is 2.5e -4 kg/m 3 s. The velocity component in the x-direction is 1.4x10- 6 m/s everywhere The velocity component in the x-direction is 1.4x10- 6 m/s everywhere

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Initial conditions Initial conditions The velocity component in the x-direction is 1.4x10-6 m/s everywhere The velocity component in the x-direction is 1.4x10-6 m/s everywhere Initial concentration is zero ppm Initial concentration is zero ppm Boundary conditions Boundary conditions The flow entering the recharge boundary at left (i.e. at x=0) is free of any contaminant; thus the concentration at that boundary is zero. The flow entering the recharge boundary at left (i.e. at x=0) is free of any contaminant; thus the concentration at that boundary is zero. All other boundaries are set to conditions of zero flux. All other boundaries are set to conditions of zero flux.

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Results Contour plots of Solute concentration (g/m 3 ) at 5 years

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Concentrations of the solute (g/m^3) at different locations in the domain Trace1 at (850m, 50m, 0.05m) Trace2 at (850m, 300m, 0.05m)

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